A numerical study of violent sloshing problems with modified MPS method

A numerical study on violent liquid sloshing phenomenon in a partially filled rectangular container is carried out by using moving particle semi-implicit(MPS) method. The present study deals with the implementation of five modifications all together over the original MPS method. The modifications include improved source terms for pressure Poisson equation, special approximation technique for the representation of gradient differential operator, collective action of mixed free surface particle identification boundary conditions, effecting Neumann boundary condition on solving the PPE and fixing judiciously the parting distance among particles to prevent collision. The suitability of the kernel function used in the original MPS method along with these five modifications is investigated for violent sloshing problems. The present model ensures a good agreement between numerical results with the existing experimental observations. The model is successfully applied to a partially filled tank undergoing horizontal sinusoidal excitation to compute the sloshing wave amplitudes and pressure on tank walls. The assessment of dynamic behaviour manifested in terms of base shear, overturning moment and impact pressure load exerted on tank ceiling induced by violent sloshing motion using MPS method is not reported in the open literature and has been efficiently carried out in the present study.     

用MPS方法数值模拟低充水液舱的晃荡

液体晃荡是一种非线性的自由面流动现象.在低充水率下,由于液体具有很大的运动空间,晃荡现象具有强烈的非线性特征,自由面的变形较大,剧烈时甚至会翻卷和破碎,这给数值模拟带来很大挑战.本文基于移动粒子半隐式法(Moving Particle Semi-Implicit,MPS)对低充水率的液舱晃荡问题进行了数值模拟.结果表明:当激励频率等于共振频率时,液体撞击到了液舱的顶板,并出现了飞溅现象,此时液体对侧舱壁产生了较大的抨击压力;在低于共振频率时,自由面出现了破碎波及波前的翻卷和融合等现象,抨击压力相对较小.计算结果表明,MPS方法能够很好地预测晃荡引起的拍击现象,数值计算得到的压力能够与实验结果很好地吻合.在自由面的追踪上,MPS方法具有很大的灵活性,能够很好地处理自由面的破碎、融合及液体的飞溅等流动现象.     

SPH方法在自由面问题中的应用

作为无网格粒子法,SPH法在处理大变形、自由面流动问题时具有显著的优势.介绍了SPH法的基本数值方法,并基于SPH法数值模拟了2个二维溃坝问题,将计算结果与试验数据进行了比较,结果表明:SPH法在处理自由面时具有很强的适应性.尽管水面发生了翻卷、破碎等剧烈的变化,但SPH法仍然能够较好地捕捉到这些流动现象,同时数值模拟得到的水头位置和自由面形状均能与试验结果相吻合,表明SPH法在处理自由面问题时具有较高的准确性及可靠性.     

Simulation of violent free surface flow by AMR method

A novel CFD approach based on adaptive mesh refinement(AMR) technique is being developed for numerical simulation of violent free surface flows. CIP method is applied to the flow solver and tangent of hyperbola for interface capturing with slope weighting(THINC/SW) scheme is implemented as the free surface capturing scheme. The PETSc library is adopted to solve the linear system. The linear solver is redesigned and modified to satisfy the requirement of the AMR mesh topology. In this paper, our CFD method is outlined and newly obtained results on numerical simulation of violent free surface flows are presented.     

带自由液面 Navier-Stokes 流动问题的ALE 分步有限元方法

将任意的拉格朗日 欧拉 (ArbitraryLagrange Euler,简称ALE)描述引入到Navier Stokes方程中 ,以速度和压力为基本变量 ,在时间域上采用分步求解格式 ,利用Galerkin加权余量法推导了分步格式的ALE有限元数值离散方程。并对带有自由液面的Navier Stokes流动问题的定解条件进行了分析讨论。最后利用所得到的ALE分步有限元方法对二维及三维不可压粘性液体大幅晃动问题进行了算例数值模拟 ,数值计算结果验证了本文方法及计算机仿真软件的正确性与可靠性     

Level-set法在液体晃荡研究中的应用

Level—set法是一种简便、通用、高效的计算分析空间运动界面的数值方法,本文尝试性地将Level—set方法应用于液体晃荡的研究,详细论述了应用该方法模拟液体晃荡的数学模型及数值解法。为了验证该方法处理晃荡问题的正确合理性,首先在势流假定下模拟了释放初始液面引起的自由晃荡,并将液面波动的数值结果与理论解析解进行了比较;然后模拟了二维矩形液箱做简谐横摇运动引起的液体受迫晃荡,计算结果以箱壁不同高度处的压强时间历经给出,并与实验结果进行了定量比较。计算结果初步表明采用Level—set方法研究液体晃荡现象是正确可行的。     

NUMERICAL SIMULATION OF TURBULENT FREE SURFACE FLOW OVER OBSTRUCTION

A two-dimensional hybrid numerical model, FEM-LES-VOF, for free surface flows is proposed in this study, which is a combination of three-step Taylor-Galerkin finite element method, large eddy simulation with the Smagorinsky sub-grid model and Computational Lagrangian-Eulerian Advection Remap Volume of Fluid （CLEAR-VOF） method. The present FEM-LES-VOF model allows the fluid flows involving violent free surface and turbulence subject to complex boundary configuration to be simulated in a straightforward manner with unstructured grids in the context of finite element method. Numerical simulation of a benchmark problem of dam breaking is conducted to verify the present model. Comparisons with experimental data show that the proposed model works well and is capable of producing reliable predictions for free surface flows. Using the FEM-LES-VOF model, the free surface flow over a semi-circular obstruction is investigated. The simulation results are compared with available experimental and numerical results. Good performance of the FEM-LES-VOF model is demonstrated again. Moreover, the numerical studies show that the turbulence plays an important role in the evolution of free surface when the reflected wave propagates upstream during the fluid flow passing the submerged obstacle.     

具有隔板容器中液体晃荡的数值模拟

在容器中装置隔板来抑制液体晃荡是一种常见的工程措施。此文针对具有隔板的矩形容器中液体晃荡问题,采用时域高阶边界元方法建立了自由水面满足完全非线性边界条件的数学模型。求解中采用了半混合欧拉-拉格朗日方法追踪流体瞬时水面,并运用四阶龙格库塔方法更新下一时间步的波面和速度势。通过与文献的数值结果的对比,验证了本模型的准确性。通过大量数值试验,研究了隔板位置、尺寸和形式等因素对容器内晃荡液体运动特性、动力特性和容器固有频率的影响。     

Numerical simulation of 3-D free surface flows by overlapping MPS

An overlapping moving particle semi-implicit(MPS) method is applied for 3-D free surface flows based on our in-house particle solver MLParticle-SJTU. In this method, the coarse particles are distributed in the whole domain and the fine particles are distributed in the local region of interest at the same time. With the fine particles being generated and removed dynamically, an algorithm of generating particles based on the 3-D overlapping volume is developed. Then, a 3-D dam break flow with an obstacle is simulated to validate the overlapping MPS. The qualitative comparison among experimental data and the results obtained by the VOF and the MPS shows that the shape of the free surface obtained by the overlapping MPS is more accurate than that obtained by the UNI-coarse and close to that obtained by the UNI-fine in the overlapping domain. In addition, the water height and the impact pressure at P1 are also in an overall agreement with experimental data. Finally, the CPU time required by the overlapping MPS is about half of that required by the UNI-fine.     

SPH方法在自由表面流体研究中的应用

对光滑粒子流体动力学法(SPH方法)的发展背景、理论基础等进行介绍,总结了SPH方法在溃坝、海冰和河冰模拟、船舶流体力学等具有自由表面的流体研究中的应用现状,认为作为一种无网格的纯Lagrange方法,SPH方法较传统的基于网格的模拟方法具有不可比拟的优势。最后分析了SPH方法的缺陷及目前研究中的不足,并就今后的研究方向和发展趋势提出自己的看法。     

CD无结构网格上的三维自由水面非静水压力流动模型Ⅱ：验证

对作者建立的CD无结构、z坐标网格上的非静水压力流动模型中的若干技术细节问题进行了进一步的阐述。提出一种改进的ELM(EulerianLagangian Method)方法求解对流项;紊流模型采用GLS(Generic Length Scale)模型,并针对急流的模拟提出一种给自由水面计算添加人工耗散以增强其稳定性的方法。通过微幅波、弯道环流、丁坝绕流3个典型算例对模型进行了基准测试,计算结果与解析解或试验资料吻合良好,表明本文模型具有能准确模拟非静水压力分布的流动和环流等的能力和良好的人工边界适应性。     

3-D numerical simulations of violent sloshing by CIP-based method

The violent sloshing flow inside a rectangular tank is computed by the CIP (Constrained Interpolation Profile) ^[1] based Cartesian grid method. Two kinds of CIP scheme, the original CIP scheme and the RCIP scheme, have been applied to the flow solver. 2-D and 3-D computations using the two CIP schemes are carried out and their performances are discussed by comparing the results of the impact pressures on the wall and the free surface profiles to the experimental measurements.

     

一种稳定的移动粒子半隐式法

该文提出了一种稳定的移动粒子半隐式法(MPS)。分析了MPS方法求解封闭区域流动的有解条件、自由面流动中粒子以较大速度撞击壁面或液面时出现的不稳定现象。为了解决这些问题,提出了Navier-Stokes方程新的求解算法和自由面边界处理方法。改进后的MPS方法提高了计算的稳定性,采用该方法成功模拟了自由面流动的溃坝现象,从而验证了该方法的有效性。     

基于MPS方法数值模拟三维LNG液舱的晃荡问题

该文基于自主开发的无网格粒子方法求解器MLParticle-SJTU,将MPS方法(moving particle semi-implicit)应用到三维LNG液舱的晃荡问题中,分别研究了LNG液舱在单自由度纵摇和横摇激励下,装载高度和激励频率对液舱晃荡作用的影响。首先,对装载高度为70%H的LNG液舱在单自由度纵摇和横摇激励下的晃荡问题分别进行了数值模拟,并将计算结果与实验结果进行比较,验证了MPS方法的可靠性。其次,对比不同装载高度,不同激励频率下液舱晃荡的拍击压力和流场分布情况,分析了装载高度和激励频率对晃荡作用的影响,并分析了一阶固有频率和共振频率随装载高度的变化规律。数值结果表明:激励频率对晃荡幅度影响较大;当激励频率在一阶固有频率附近时,会发生剧烈的晃荡现象;52.5%H为危险装载高度,在共振频率下,产生的拍击压力最大。     

自由液面流体大晃动有限元方法

本文给出了一种以ALE描述N-S方程为基础的,求解具有自由液面流体大晃动的有限元方法.文中首先给了ALE描述的N-S方程、自由液面边界条件和相应的有限元方程;然后分别采用经典Galerkin格式和Newmark法进行空间和时域的离散化,得到了相的Newmark-压力修正求解格式,并由预测-校正法直接求解.分析实例表明这是一种简单可靠的方法.     

Level Set方法求解三维大幅晃动问题的分步有限元法

取与容器固结的坐标系,将外激励视为质量力,针对刚性容器内流体三维非线性大幅晃动问题,提出了在时间和空间上均具有二阶精度的两步Taylor—Galerkin分步有限元方法。该法首先显式地求解忽略压力梯度项的中间速度场,然后由压力泊松方程求得压力场,再根据求得的压力对速度场进行修正。求解中利用Level—Set方法隐式地追踪自由面,即在每个时间步求解Level—Set函数随水流的输运方程,并通过迭代的方法对其进行重新初始化,以保持为距离的函数,从而达到捕捉自由面的目的。控制方程统一采用简单方便且具有较高精度的两步Taylor—Galerkin格式进行离散,并通过两个算例验证了本文数值方法的正确性和有效性。     

Numerical simulation of hydro-elastic problems with smoothed particle hydrodynamics method

Violent free surface flows with strong fluid-solid interactions can produce a tremendous pressure load on structures, resu-lting in elastic and even plastic deformations. Modeling hydro-elastic problem...     

带自由表面后向台阶流的数值模拟研究

后向台阶流是工程领域中一类常见的流动现象,也是流体力学中复杂剪切流动的一个典型例子。针对自由表面对后向台阶流场的影响,在总结前人研究成果的基础上,本文利用VOF方法追踪自由表面,采用realizable k-ε紊流模型封闭控制方程,建立立面二维数值模型,对带自由表面后向台阶流进行了模拟研究。模拟得到4种特征雷诺数工况下,台阶后纵向流速、紊动能、耗散率、边界压力值和水面流速的沿程分布。模拟结果与原型实验观测结果吻合较好。根据模拟结果,对台阶后流场随特征雷诺数变化的规律以及自由水面对台阶后流场分布、漩涡结构和压力值的影响进行了分析讨论。     

NUMERICAL SIMULATION OF SLOSHING IN RECTANGULAR TANK WITH VOF BASED ON UNSTRUCTURED GRIDS

A new method for sloshing simulation in a sway tank is present, in which the two phase interface is treated as a physical discontinuity, which can be captured by a well-designed high order scheme. Based on Normalized Variable Diagram (NVD), a high order discretization scheme with unstructured grids is realized, together with a numerical method for free surface flow with a fixed grid. This method is implemented in an in-house code General Transport Equation Analyzer (GTEA) which is an unstructured grids finite volume solver. The present method is first validated by available analytical solutions. A simulation for a 2-D rectangular tank at different excitation frequencies of the sway is carried out. A comparison with experimental data in literature and results obtained by commercial software CFX shows that the sloshing load on the monitor points agrees well with the experimental data, with the same grids, and the present method gives better results on the secondary peak. It is shown that the present method can simulate the free surface overturning and breakup phenomena.     

二维滑坡涌浪的SPH方法数值模拟

块体滑坡往往引起自由水面的剧烈变化,研究块体滑坡激发的水面波动一直是水利与海岸工程界非常感兴趣的问题。该文使用SPH方法（光滑质点水动力学）对水下块体下滑引起的自由表面水动力学过程进行了二维数值模拟,并将数值计算结果与试验数据作了对比,计算结果给出了块体下滑过程中,水体表面出现的二次卷破现象,以及在块体上方出现两个方向相反的旋涡,显示了SPH方法对处理块体下滑引起的自由表面大变形问题具有十分优越的特性。通过数值试验,文中还讨论了滑块下滑速度对自由表面破碎和形成的旋涡个数的影响。